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We obtain a characterization of complete interpolating sequences in a class of Fock-type spaces with radial weights for which such sequences exist. Our criterion is formulated in terms of logarithmic separation and controlled perturbations…

Complex Variables · Mathematics 2026-03-25 Karim Kellay , Youssef Omari

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert…

Functional Analysis · Mathematics 2022-05-18 Simon N. Chandler-Wilde , David P. Hewett , Andrea Moiola

A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike…

Numerical Analysis · Mathematics 2018-07-16 D. Ramos-Lopez , M. A. Sanchez-Granero , M. Fernandez-Martinez , A. Martinez-Finkelshtein

This paper explores the generalization of the method for extracting Riemann trigonometric B-splines and Riemann kernels of trigonometric interpolation splines of arbitrary order on different grids of stitching and interpolation. It is…

Numerical Analysis · Mathematics 2023-11-23 Volodymyr Denysiuk , Olena Hryshko

This paper extends the known characterization of interpolation and sampling sequences for Bergman spaces to the mixed-norm spaces. The Bergman spaces have conformal invariance properties not shared by the mixed-norm spaces. As a result,…

Complex Variables · Mathematics 2018-01-25 Phuc K. Nguyen , Daniel H. Luecking

This paper focuses on the use of the theory of Reproducing Kernel Hilbert Spaces in the statistical analysis of replicated point processes. We show that spatial point processes can be observed as random variables in a Reproducing Kernel…

Methodology · Statistics 2023-01-06 Amelia Simó

The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…

Numerical Analysis · Mathematics 2017-05-03 Giampietro Allasia , Roberto Cavoretto , Alessandra De Rossi

We develop novel learning rates for conditional mean embeddings by applying the theory of interpolation for reproducing kernel Hilbert spaces (RKHS). We derive explicit, adaptive convergence rates for the sample estimator under the…

Machine Learning · Statistics 2026-04-09 Prem Talwai , Ali Shameli , David Simchi-Levi

We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size…

Functional Analysis · Mathematics 2022-05-04 José Luis Romero , Jordy Timo van Velthoven , Felix Voigtlaender

The interpolation of couples of separable Hilbert spaces with a function parameter is studied. The main properties of the classic interpolation are proved. Some applications to the interpolation of isotropic H\"ormander spaces over a closed…

Analysis of PDEs · Mathematics 2009-03-30 Vladimir A. Mikhailets , Alexandr A. Murach

We studied complex interpolation noncommutative Hardy space associated with semi-finite von Neumann algebra and extend Pisier's interpolation theorem for this case.

Operator Algebras · Mathematics 2019-05-01 Turdebek N. Bekjan , Kordan N. Ospanov

Reproducing kernel Hilbert spaces (RKHSs) are very important function spaces, playing an important role in machine learning, statistics, numerical analysis and pure mathematics. Since Lipschitz and H\"older continuity are important…

Functional Analysis · Mathematics 2023-10-30 Christian Fiedler

After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in $\mathbb{C}^n$, as well as the…

Functional Analysis · Mathematics 2024-12-17 Gilbert J. Groenewald , Sanne ter Horst , Hugo J. Woerdeman

Classical convergence analysis for kernel interpolation typically assumes that the target function $f$ lies in the reproducing kernel Hilbert space $\mathcal{H}_k\!\left(\Omega\right)$ induced by a kernel on a domain…

Numerical Analysis · Mathematics 2025-12-09 Tobias Ehring , Max-Paul Vogel , Bernard Haasdonk

We denote by $\Hp$ the Hilbert space of ordinary Dirichlet series with square-summable coefficients. The main result is that a bounded sequence of points in the half-plane $\sigma >1/2$ is an interpolating sequence for $\Hp$ if and only if…

Complex Variables · Mathematics 2012-10-17 Jan-Fredrik Olsen , Kristian Seip

A general interpolation problem with operator argument is studied for functions f from the de Branges-Rovnyak space H(s) associated with an analytic function s mapping the open unit disk D into the closed unit disk. The interpolation…

Functional Analysis · Mathematics 2018-04-24 Joseph A. Ball , Vladimir Bolotnikov , Sanne Ter Horst

In this paper we study nonlinear interpolation problems for interpolation and peak-interpolation sets of function algebras. The subject goes back to the classical Rudin-Carleson interpolation theorem. In particular, we prove the following…

Complex Variables · Mathematics 2021-06-15 Alexander Brudnyi

We present a method to reconstruct the dielectric susceptibility (scattering potential) of an inhomogeneous scattering medium, based on the solution to the inverse scattering problem with internal sources. We employ the theory of…

Numerical Analysis · Mathematics 2024-07-18 Yakun Dong , Kamran Sadiq , Otmar Scherzer , John C. Schotland

Bitangential interpolation problems in the class of matrix valued functions in the generalized Schur class are considered in both the open unit disc and the open right half plane, including problems in which the solutions is not assumed to…

Classical Analysis and ODEs · Mathematics 2011-02-22 Vladimir Derkach , Harry Dym

In this article we present a modified S-iteration process that we combine with inertial extrapolation to find a common solution to the split monotone inclusion problem and the fixed point problem in real Hilbert space.Our goal is to…

Numerical Analysis · Mathematics 2021-10-11 Shamshad Husain , Uqba Rafat